and the same component-wise arithmetic operations and relations as defined in [1]}, we reach the decomposition
\({\bf V}_N^k=\bigoplus _{\begin{array}{c} |\mathbf {l}|_\infty \le N\\\mathbf {l}\in \mathbb {N}_0^d\end{array}} \mathbf {W}_\mathbf {l}^k.\) 
